Chapter 11 : Impulse Turbine

Example 11.1 Page No : 233

In [1]:
# Variables
P = 8820.*1000
N = 600./60
H = 500.
Cv = 0.97
Cu = 0.46
no = 0.85
w = 9810.
g = 9.81

# Calculations 
Q = P/(no*w*H)
V1 = Cv*((2*g*H)**0.5)
u = Cu*V1
D = u/(3.142*N)
d = D/15
a = 3.142*d*d/4
n = Q/(a*V1)
n1 = round(n+1)

# Results 
print "discharge in m3/sec,wheel diameter in m, jet diameter in cm, number os jets ",round(Q,6),round(D,4),round(d*100,2),n1

discharge in m3/sec,wheel diameter in m, jet diameter in cm, number os jets  2.115488 1.4066 9.38 4.0

Example 11.2 Page No : 235

In [3]:
import math 

# Variables
H = 46.
Q = 1.
u1 = 15.
y = 165.
y2 = 180-y
Cv = 0.975
g = 9.81

# Calculations 
V1 = ((2*g*H)**0.5)
Vw1 = V1
Vr1 = V1-u1
Vr2 = Vr1
Vw2 = (Vr2*(math.cos(math.radians(y2))))-u1
w = 9810.
P = (w*Q*(Vw1+Vw2)*u1)/(g*1000)
n = P*1000/(w*Q*H)

# Results 
print "power developed in Kw and efficiency of the wheel",round(P,3),round((n*100),3)

power developed in Kw and efficiency of the wheel 443.571 98.296

Example 11.3 Page No : 236

In [4]:
import math 

# Variables
H = 340.
P = 4410.*1000
N = 500./60
Cv = 0.97
no = 0.86
w = 9810.
g = 9.81

# Calculations 
Q = P/(w*H*no)
V1 = Cv*(math.sqrt(2*g*H))
u = 0.45*V1
D = u/(3.142*N)
a = Q/V1

# Results 
print "mean diameter in m,jet area in m2",round(D,4),round(a,7)

mean diameter in m,jet area in m2 1.3616 0.0194058

Example 11.4 Page No : 237

In [4]:
import math 

# Variables
H = 45.
Q = 50./60
u1 = 12.5
y = 160.
y2 = 180.-y
Cv = 0.97
g = 9.81

# Calculations and Results
V1 = Cv*((2*g*H)**0.5)
Vw1 = V1
Vr1 = V1-u1
Vr2 = Vr1
Vw2 = Vr2*(math.cos(math.radians(y2)))-u1
w = 9810
P = (w*Q*(Vw1+Vw2)*u1)/(g*1000)
nh = (2*u1*(Vw1+Vw2))/(V1*V1)
print "power developed in Kw and hydraulic efficiency",P,nh*100

H1 = 50
V11 = Cv*((2*g*H1)**0.5)
Vw11 = V11
Vr11 = V11-u1
Vr21 = Vr11
Vw21 = Vr21*(math.cos(math.radians(y2)))-u1
w = 9810
P = (w*Q*(Vw11+Vw21)*u1)/(g*1000)
print "Power developed in Kw if head is increased to 50",P

power developed in Kw and hydraulic efficiency 329.792686546 95.2790189845
Power developed in Kw if head is increased to 50 361.293854458

Example 11.5 Page No : 237

In [5]:
import math

# Variables
H = 50.
Q = 1.2
u1 = 18.
y = 160.
y2 = 180-y
Cv = 0.94
g = 9.81

# Calculations 
V1 = Cv*((2*g*H)**0.5)
Vw1 = V1
Vr1 = V1-u1
Vr2 = Vr1
Vw2 = Vr2*(math.cos(math.radians(y2)))-u1
w = 9810
P = (w*Q*(Vw1+Vw2)*u1)/(g*1000)
n = P*1000/(w*Q*H)

# Results 
print "power developed in Kw and efficiency of the wheel",P,n*100

power developed in Kw and efficiency of the wheel 479.375537454 81.4433464923

Example 11.6 Page No : 238

In [2]:
import math 

# Variables
D = 1.
N = 1000./60
H = 700.
y = 165.
y2 = 180-y
Q = 0.1
Cv = 0.97
g = 9.81

# Calculations 
u = D*math.pi*N
V1 = Cv*(math.sqrt(2*g*H))
nh = (2*u*(V1-u)*(1+(math.cos(math.radians(y2)))))/(V1*V1)

# Results 
print "hydraulic efficiency of the wheel",round((nh*100),2),"%"

# note : rounding off error

hydraulic efficiency of the wheel 97.69 %

Example 11.7 Page No : 239

In [7]:
import math 

# Variables
Hg = 500.
hf = Hg/3
H = Hg-hf
Q = 2.
y = 165.
y2 = 180.-y
g = 9.81
w = 9810.
Cv = 1.

# Calculations 
V1 = Cv*(math.sqrt(2*g*H))
u = 0.45*V1
Vr1 = V1-u
Vw1 = V1
Vr2 = Vr1
Vw2 = (Vr2*(math.cos(math.radians(y2))))-u
W = w*Q*(Vw1+Vw2)*u/g
P = W/1000
nh = 2*u*(Vw1+Vw2)/(V1*V1)

# Results 
print "power given by the water to the runner in Kw : %.3f \
\nHydraulic efficiency %.2f"%(P,(nh*100)),"%"

# note : rounding off error

power given by the water to the runner in Kw : 6364.292 
Hydraulic efficiency 97.31 %

Example 11.8 Page No : 240

In [11]:
import math 

# Variables
L = 1600.
H = 550.
Dp = 1.2
d = 0.18
f = 0.006
Cv = 0.97
g = 9.81

# Calculations 
V1 = Cv*(math.sqrt(2*g*H))
a = math.pi*d*d/4
Q = a*V1
w = 9810
P = (w*Q*V1*V1)/(2*g*1000)
ap = math.pi*Dp*Dp/4
Vp = Q/ap
Hf = (4*f*L*Vp*Vp)/(Dp*2*g)
Tp = 4*w*Q*(H+Hf)/1000

# Results 
print "power to each jet in Kw : %.1f \
\ntotal power at reserviour i Kw : %.2f"%(P,Tp)

# note : rounding off error.

power to each jet in Kw : 13017.1 
total power at reserviour i Kw : 56182.23

Example 11.9 Page No : 241

In [12]:
import math 

# Variables
Q = 4.
H = 250.
L = 3000.
n1 = 4.
n = 0.91
nh = 0.9
Cv = 0.975
f4 = 0.0045

# Calculations 
hf = H-H*n
Hn = H-hf
g = 9.81
w = 9810
V1 = Cv*(math.sqrt(2*g*Hn))
Pw = w*Q*V1*V1/(2*g*1000)
Pt = nh*Pw
q = Q/n1
d = math.sqrt(4*q/(3.142*V1))
D = ((f4*L*16*16)/(2*g*3.142*3.142*hf))**0.2

# Results 
print "power developed by turbine in Kw :  %.1f \
\ndiameter jet and diameter of pipeline"%(Pt),round(d,4),round(D,4)

power developed by turbine in Kw :  7637.7 
diameter jet and diameter of pipeline 0.1398 0.9547
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